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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 25 May 2012 07:47:05 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/25/t1337946448tck9waea95x6cko.htm/, Retrieved Sat, 04 May 2024 03:58:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167471, Retrieved Sat, 04 May 2024 03:58:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact104

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-05-25 11:47:05] [90784e9e55228384d12d0fe678c8bac5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
65
65,3
62,9
63,5
62,1
59,3
61,6
61,5
60,1
59,5
62,7
65,5
63,8
63,8
62,7
62,3
62,4
64,8
66,4
65,1
67,4
68,8
68,6
71,5
75
84,3
84
79,1
78,8
82,7
85,3
84,5
80,8
70,1
68,2
68,1
72,3
73,1
71,5
74,1
80,3
80,6
81,4
87,4
89,3
93,2
92,8
96,8
100,3
95,6
89
87,4
86,7
92,8
98,6
100,8
105,5
107,8
113,7
120,3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167471&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167471&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167471&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0187838542206062
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0187838542206062 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167471&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0187838542206062[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167471&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167471&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0187838542206062
gamma0






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1363.863.09369393575230.706306064247656
1463.863.75193334157920.0480666584208436
1562.762.55122737597230.148772624027686
1662.361.92623764643670.373762353563301
1762.462.09235208608830.307647913911744
1864.864.62517107567940.174828924320579
1966.464.89835976467741.50164023532263
2065.166.7590509475527-1.6590509475527
2167.463.99955982171613.40044017828387
2268.867.15931652552741.64068347447262
2368.672.9661027431291-4.36610274312908
2471.571.7395636341269-0.239563634126924
257569.50606720817955.49393279182047
2684.375.02284656923859.27715343076146
278482.85278047880711.14721952119292
2879.183.1748126515922-4.07481265159221
2978.878.9819309693183-0.18193096931833
3082.781.75110080502960.948899194970394
3185.382.97551359707122.32448640292877
3284.585.9160106751087-1.41601067510872
3380.883.2320489563062-2.43204895630625
3470.180.5796646316997-10.4796646316997
3568.274.2461680136315-6.04616801363153
3668.171.1961211452563-3.09612114525629
3772.366.0420002939226.25799970607804
3873.172.1781053626560.921894637344039
3971.571.6155541944857-0.115554194485668
4074.170.56124081084793.53875918915205
4180.373.84028673477226.45971326522782
4280.683.2374705881872-2.63747058818716
4381.480.75621266378530.643787336214714
4487.481.85726291594765.54273708405243
4589.386.04252209111073.25747790888933
4693.289.08211453714814.11788546285186
4792.898.9760710696663-6.17607106966635
4896.897.1804942169822-0.380494216982157
49100.394.22816991298986.07183008701024
5095.6100.439220995964-4.83922099596415
518993.8703385557882-4.87033855578815
5287.487.9702079995864-0.570207999586401
5386.787.1611504695597-0.461150469559669
5492.889.83274702348282.96725297651724
5598.693.0191598269335.58084017306702
56100.899.25759057223111.54240942776889
57105.599.27183125382086.22816874617918
58107.8105.3090912708992.49090872910099
59113.7114.521446990503-0.821446990503006
60120.3119.1908385079411.10916149205939

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 63.8 & 63.0936939357523 & 0.706306064247656 \tabularnewline
14 & 63.8 & 63.7519333415792 & 0.0480666584208436 \tabularnewline
15 & 62.7 & 62.5512273759723 & 0.148772624027686 \tabularnewline
16 & 62.3 & 61.9262376464367 & 0.373762353563301 \tabularnewline
17 & 62.4 & 62.0923520860883 & 0.307647913911744 \tabularnewline
18 & 64.8 & 64.6251710756794 & 0.174828924320579 \tabularnewline
19 & 66.4 & 64.8983597646774 & 1.50164023532263 \tabularnewline
20 & 65.1 & 66.7590509475527 & -1.6590509475527 \tabularnewline
21 & 67.4 & 63.9995598217161 & 3.40044017828387 \tabularnewline
22 & 68.8 & 67.1593165255274 & 1.64068347447262 \tabularnewline
23 & 68.6 & 72.9661027431291 & -4.36610274312908 \tabularnewline
24 & 71.5 & 71.7395636341269 & -0.239563634126924 \tabularnewline
25 & 75 & 69.5060672081795 & 5.49393279182047 \tabularnewline
26 & 84.3 & 75.0228465692385 & 9.27715343076146 \tabularnewline
27 & 84 & 82.8527804788071 & 1.14721952119292 \tabularnewline
28 & 79.1 & 83.1748126515922 & -4.07481265159221 \tabularnewline
29 & 78.8 & 78.9819309693183 & -0.18193096931833 \tabularnewline
30 & 82.7 & 81.7511008050296 & 0.948899194970394 \tabularnewline
31 & 85.3 & 82.9755135970712 & 2.32448640292877 \tabularnewline
32 & 84.5 & 85.9160106751087 & -1.41601067510872 \tabularnewline
33 & 80.8 & 83.2320489563062 & -2.43204895630625 \tabularnewline
34 & 70.1 & 80.5796646316997 & -10.4796646316997 \tabularnewline
35 & 68.2 & 74.2461680136315 & -6.04616801363153 \tabularnewline
36 & 68.1 & 71.1961211452563 & -3.09612114525629 \tabularnewline
37 & 72.3 & 66.042000293922 & 6.25799970607804 \tabularnewline
38 & 73.1 & 72.178105362656 & 0.921894637344039 \tabularnewline
39 & 71.5 & 71.6155541944857 & -0.115554194485668 \tabularnewline
40 & 74.1 & 70.5612408108479 & 3.53875918915205 \tabularnewline
41 & 80.3 & 73.8402867347722 & 6.45971326522782 \tabularnewline
42 & 80.6 & 83.2374705881872 & -2.63747058818716 \tabularnewline
43 & 81.4 & 80.7562126637853 & 0.643787336214714 \tabularnewline
44 & 87.4 & 81.8572629159476 & 5.54273708405243 \tabularnewline
45 & 89.3 & 86.0425220911107 & 3.25747790888933 \tabularnewline
46 & 93.2 & 89.0821145371481 & 4.11788546285186 \tabularnewline
47 & 92.8 & 98.9760710696663 & -6.17607106966635 \tabularnewline
48 & 96.8 & 97.1804942169822 & -0.380494216982157 \tabularnewline
49 & 100.3 & 94.2281699129898 & 6.07183008701024 \tabularnewline
50 & 95.6 & 100.439220995964 & -4.83922099596415 \tabularnewline
51 & 89 & 93.8703385557882 & -4.87033855578815 \tabularnewline
52 & 87.4 & 87.9702079995864 & -0.570207999586401 \tabularnewline
53 & 86.7 & 87.1611504695597 & -0.461150469559669 \tabularnewline
54 & 92.8 & 89.8327470234828 & 2.96725297651724 \tabularnewline
55 & 98.6 & 93.019159826933 & 5.58084017306702 \tabularnewline
56 & 100.8 & 99.2575905722311 & 1.54240942776889 \tabularnewline
57 & 105.5 & 99.2718312538208 & 6.22816874617918 \tabularnewline
58 & 107.8 & 105.309091270899 & 2.49090872910099 \tabularnewline
59 & 113.7 & 114.521446990503 & -0.821446990503006 \tabularnewline
60 & 120.3 & 119.190838507941 & 1.10916149205939 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167471&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]63.8[/C][C]63.0936939357523[/C][C]0.706306064247656[/C][/ROW]
[ROW][C]14[/C][C]63.8[/C][C]63.7519333415792[/C][C]0.0480666584208436[/C][/ROW]
[ROW][C]15[/C][C]62.7[/C][C]62.5512273759723[/C][C]0.148772624027686[/C][/ROW]
[ROW][C]16[/C][C]62.3[/C][C]61.9262376464367[/C][C]0.373762353563301[/C][/ROW]
[ROW][C]17[/C][C]62.4[/C][C]62.0923520860883[/C][C]0.307647913911744[/C][/ROW]
[ROW][C]18[/C][C]64.8[/C][C]64.6251710756794[/C][C]0.174828924320579[/C][/ROW]
[ROW][C]19[/C][C]66.4[/C][C]64.8983597646774[/C][C]1.50164023532263[/C][/ROW]
[ROW][C]20[/C][C]65.1[/C][C]66.7590509475527[/C][C]-1.6590509475527[/C][/ROW]
[ROW][C]21[/C][C]67.4[/C][C]63.9995598217161[/C][C]3.40044017828387[/C][/ROW]
[ROW][C]22[/C][C]68.8[/C][C]67.1593165255274[/C][C]1.64068347447262[/C][/ROW]
[ROW][C]23[/C][C]68.6[/C][C]72.9661027431291[/C][C]-4.36610274312908[/C][/ROW]
[ROW][C]24[/C][C]71.5[/C][C]71.7395636341269[/C][C]-0.239563634126924[/C][/ROW]
[ROW][C]25[/C][C]75[/C][C]69.5060672081795[/C][C]5.49393279182047[/C][/ROW]
[ROW][C]26[/C][C]84.3[/C][C]75.0228465692385[/C][C]9.27715343076146[/C][/ROW]
[ROW][C]27[/C][C]84[/C][C]82.8527804788071[/C][C]1.14721952119292[/C][/ROW]
[ROW][C]28[/C][C]79.1[/C][C]83.1748126515922[/C][C]-4.07481265159221[/C][/ROW]
[ROW][C]29[/C][C]78.8[/C][C]78.9819309693183[/C][C]-0.18193096931833[/C][/ROW]
[ROW][C]30[/C][C]82.7[/C][C]81.7511008050296[/C][C]0.948899194970394[/C][/ROW]
[ROW][C]31[/C][C]85.3[/C][C]82.9755135970712[/C][C]2.32448640292877[/C][/ROW]
[ROW][C]32[/C][C]84.5[/C][C]85.9160106751087[/C][C]-1.41601067510872[/C][/ROW]
[ROW][C]33[/C][C]80.8[/C][C]83.2320489563062[/C][C]-2.43204895630625[/C][/ROW]
[ROW][C]34[/C][C]70.1[/C][C]80.5796646316997[/C][C]-10.4796646316997[/C][/ROW]
[ROW][C]35[/C][C]68.2[/C][C]74.2461680136315[/C][C]-6.04616801363153[/C][/ROW]
[ROW][C]36[/C][C]68.1[/C][C]71.1961211452563[/C][C]-3.09612114525629[/C][/ROW]
[ROW][C]37[/C][C]72.3[/C][C]66.042000293922[/C][C]6.25799970607804[/C][/ROW]
[ROW][C]38[/C][C]73.1[/C][C]72.178105362656[/C][C]0.921894637344039[/C][/ROW]
[ROW][C]39[/C][C]71.5[/C][C]71.6155541944857[/C][C]-0.115554194485668[/C][/ROW]
[ROW][C]40[/C][C]74.1[/C][C]70.5612408108479[/C][C]3.53875918915205[/C][/ROW]
[ROW][C]41[/C][C]80.3[/C][C]73.8402867347722[/C][C]6.45971326522782[/C][/ROW]
[ROW][C]42[/C][C]80.6[/C][C]83.2374705881872[/C][C]-2.63747058818716[/C][/ROW]
[ROW][C]43[/C][C]81.4[/C][C]80.7562126637853[/C][C]0.643787336214714[/C][/ROW]
[ROW][C]44[/C][C]87.4[/C][C]81.8572629159476[/C][C]5.54273708405243[/C][/ROW]
[ROW][C]45[/C][C]89.3[/C][C]86.0425220911107[/C][C]3.25747790888933[/C][/ROW]
[ROW][C]46[/C][C]93.2[/C][C]89.0821145371481[/C][C]4.11788546285186[/C][/ROW]
[ROW][C]47[/C][C]92.8[/C][C]98.9760710696663[/C][C]-6.17607106966635[/C][/ROW]
[ROW][C]48[/C][C]96.8[/C][C]97.1804942169822[/C][C]-0.380494216982157[/C][/ROW]
[ROW][C]49[/C][C]100.3[/C][C]94.2281699129898[/C][C]6.07183008701024[/C][/ROW]
[ROW][C]50[/C][C]95.6[/C][C]100.439220995964[/C][C]-4.83922099596415[/C][/ROW]
[ROW][C]51[/C][C]89[/C][C]93.8703385557882[/C][C]-4.87033855578815[/C][/ROW]
[ROW][C]52[/C][C]87.4[/C][C]87.9702079995864[/C][C]-0.570207999586401[/C][/ROW]
[ROW][C]53[/C][C]86.7[/C][C]87.1611504695597[/C][C]-0.461150469559669[/C][/ROW]
[ROW][C]54[/C][C]92.8[/C][C]89.8327470234828[/C][C]2.96725297651724[/C][/ROW]
[ROW][C]55[/C][C]98.6[/C][C]93.019159826933[/C][C]5.58084017306702[/C][/ROW]
[ROW][C]56[/C][C]100.8[/C][C]99.2575905722311[/C][C]1.54240942776889[/C][/ROW]
[ROW][C]57[/C][C]105.5[/C][C]99.2718312538208[/C][C]6.22816874617918[/C][/ROW]
[ROW][C]58[/C][C]107.8[/C][C]105.309091270899[/C][C]2.49090872910099[/C][/ROW]
[ROW][C]59[/C][C]113.7[/C][C]114.521446990503[/C][C]-0.821446990503006[/C][/ROW]
[ROW][C]60[/C][C]120.3[/C][C]119.190838507941[/C][C]1.10916149205939[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167471&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167471&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1363.863.09369393575230.706306064247656
1463.863.75193334157920.0480666584208436
1562.762.55122737597230.148772624027686
1662.361.92623764643670.373762353563301
1762.462.09235208608830.307647913911744
1864.864.62517107567940.174828924320579
1966.464.89835976467741.50164023532263
2065.166.7590509475527-1.6590509475527
2167.463.99955982171613.40044017828387
2268.867.15931652552741.64068347447262
2368.672.9661027431291-4.36610274312908
2471.571.7395636341269-0.239563634126924
257569.50606720817955.49393279182047
2684.375.02284656923859.27715343076146
278482.85278047880711.14721952119292
2879.183.1748126515922-4.07481265159221
2978.878.9819309693183-0.18193096931833
3082.781.75110080502960.948899194970394
3185.382.97551359707122.32448640292877
3284.585.9160106751087-1.41601067510872
3380.883.2320489563062-2.43204895630625
3470.180.5796646316997-10.4796646316997
3568.274.2461680136315-6.04616801363153
3668.171.1961211452563-3.09612114525629
3772.366.0420002939226.25799970607804
3873.172.1781053626560.921894637344039
3971.571.6155541944857-0.115554194485668
4074.170.56124081084793.53875918915205
4180.373.84028673477226.45971326522782
4280.683.2374705881872-2.63747058818716
4381.480.75621266378530.643787336214714
4487.481.85726291594765.54273708405243
4589.386.04252209111073.25747790888933
4693.289.08211453714814.11788546285186
4792.898.9760710696663-6.17607106966635
4896.897.1804942169822-0.380494216982157
49100.394.22816991298986.07183008701024
5095.6100.439220995964-4.83922099596415
518993.8703385557882-4.87033855578815
5287.487.9702079995864-0.570207999586401
5386.787.1611504695597-0.461150469559669
5492.889.83274702348282.96725297651724
5598.693.0191598269335.58084017306702
56100.899.25759057223111.54240942776889
57105.599.27183125382086.22816874617918
58107.8105.3090912708992.49090872910099
59113.7114.521446990503-0.821446990503006
60120.3119.1908385079411.10916149205939






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61117.241913924896109.690949288188124.792878561604
62117.452400127128106.703369730717128.201430523538
63115.44243564632102.359930809288128.524940483352
64114.2966914803899.179529930353129.413853030407
65114.18151443444897.1486534342284131.214375434669
66118.51769921290599.116224397572137.919174028238
67118.95547682303997.8743763683575140.036577277721
68119.81805073313997.0686715576826142.567429908596
69118.04672072814194.1724031848356141.921038271446
70117.79336019542992.5657300594378143.020990331421
71125.06321707077296.9687992350436153.157634906501
72131.0363124870699.8247898927558162.247835081364

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 117.241913924896 & 109.690949288188 & 124.792878561604 \tabularnewline
62 & 117.452400127128 & 106.703369730717 & 128.201430523538 \tabularnewline
63 & 115.44243564632 & 102.359930809288 & 128.524940483352 \tabularnewline
64 & 114.29669148038 & 99.179529930353 & 129.413853030407 \tabularnewline
65 & 114.181514434448 & 97.1486534342284 & 131.214375434669 \tabularnewline
66 & 118.517699212905 & 99.116224397572 & 137.919174028238 \tabularnewline
67 & 118.955476823039 & 97.8743763683575 & 140.036577277721 \tabularnewline
68 & 119.818050733139 & 97.0686715576826 & 142.567429908596 \tabularnewline
69 & 118.046720728141 & 94.1724031848356 & 141.921038271446 \tabularnewline
70 & 117.793360195429 & 92.5657300594378 & 143.020990331421 \tabularnewline
71 & 125.063217070772 & 96.9687992350436 & 153.157634906501 \tabularnewline
72 & 131.03631248706 & 99.8247898927558 & 162.247835081364 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167471&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]61[/C][C]117.241913924896[/C][C]109.690949288188[/C][C]124.792878561604[/C][/ROW]
[ROW][C]62[/C][C]117.452400127128[/C][C]106.703369730717[/C][C]128.201430523538[/C][/ROW]
[ROW][C]63[/C][C]115.44243564632[/C][C]102.359930809288[/C][C]128.524940483352[/C][/ROW]
[ROW][C]64[/C][C]114.29669148038[/C][C]99.179529930353[/C][C]129.413853030407[/C][/ROW]
[ROW][C]65[/C][C]114.181514434448[/C][C]97.1486534342284[/C][C]131.214375434669[/C][/ROW]
[ROW][C]66[/C][C]118.517699212905[/C][C]99.116224397572[/C][C]137.919174028238[/C][/ROW]
[ROW][C]67[/C][C]118.955476823039[/C][C]97.8743763683575[/C][C]140.036577277721[/C][/ROW]
[ROW][C]68[/C][C]119.818050733139[/C][C]97.0686715576826[/C][C]142.567429908596[/C][/ROW]
[ROW][C]69[/C][C]118.046720728141[/C][C]94.1724031848356[/C][C]141.921038271446[/C][/ROW]
[ROW][C]70[/C][C]117.793360195429[/C][C]92.5657300594378[/C][C]143.020990331421[/C][/ROW]
[ROW][C]71[/C][C]125.063217070772[/C][C]96.9687992350436[/C][C]153.157634906501[/C][/ROW]
[ROW][C]72[/C][C]131.03631248706[/C][C]99.8247898927558[/C][C]162.247835081364[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167471&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167471&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61117.241913924896109.690949288188124.792878561604
62117.452400127128106.703369730717128.201430523538
63115.44243564632102.359930809288128.524940483352
64114.2966914803899.179529930353129.413853030407
65114.18151443444897.1486534342284131.214375434669
66118.51769921290599.116224397572137.919174028238
67118.95547682303997.8743763683575140.036577277721
68119.81805073313997.0686715576826142.567429908596
69118.04672072814194.1724031848356141.921038271446
70117.79336019542992.5657300594378143.020990331421
71125.06321707077296.9687992350436153.157634906501
72131.0363124870699.8247898927558162.247835081364


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')